Why in CFAI MBS examples are the OAS’ always greater than the Z-Spreads? I would have thought that the MBS, because of its prepayment option (unfavorable to the investor) would be cheaper than a straight bond? Here is a simplified example: Assume the yield curve is flat at 10%- So the Z-spread equals the nominal spread. A straight 2 year bond with $100 (10%) coupon payments is trading for $1000. Coupons payable annually. The Z-Spread would equal: 1000 = 100/ (1+Z)^1 + 100/ (1+Z)^2 + 1000/ (1+Z)^2 Z= 10% or 1000bp I would think the MBS would have a lower price than the straight bond as it can be prepaid at any time by the holder. (But this may be where I’m wrong) So let’s say the price of the MBS is $966.2 966.2 = 100/ (1+OAS)^1 + 100/ (1+OAS)^2 + 1000/(1+OAS)^2 The OAS value would equal 12% or 1200bp Then the value of the option would equal Z-Spread - OAS = -200bp But the CFAI always shows the option cost on MBS as positive. The only reason I can think of is that the CFAI text is comparing a MBS with a call option, to a MBS security without a call option. Can you even have a call option on a MBS? Any help or thoughts would be most appreciated.

This doesn’t sound right. OAS for MBS is the spread that you add to every nodes in a Monte Carlo simulated binomial tree. (Hence, the OAS for MBS is the average spread that you add to treasury spot rates.) The way you evaluate a MBS using a single interest rate path doesn’t seem right to me.

You may be correct: I was thinking that a monte carlo model is used to determine the price of the bond then the OAS is just calculated from that price. So that you can compare it to the treasury curve. So under your reasoning does the option add value to the MBS or reduce value?

OAS>Z because option is held by the seller of the MBS. i.e. the homeowners have a right to prepay, so buyers of the MBS have to be compensated for selling this option, this occurs via a higher spread.

Page 462 CFAI text on alternative investments shows the OAS< Z-Spread. Why?

Sorry, sorry, sorry my brain is fried today and I was running to a meeting earlier, lets break this down: In an MBS composed of just one home loan we have: Issuer: Homeowner issues ‘bond’ to finance his house, he can call that bond at any time (typically when rates drop) and refinance, this is a valuable call option for him to have and one that the buyer of the MBS must be compensated for writing. Investor: whoever buys the MBS security and holds it, this person has written a call option on the bond and is effectively short the call he gets a premium for ‘writing’ this call. So we have the following that must hold OASoas this result is an impossibility, i.e the OAS calc should yield a value 1000 (if zpread yields 1000). This should make sense since when you use the zspread without adjusting out the option cost the bond seems cheap to where its trading, this is the case because you haven’t compensated for the call option that is embedded in that bond so it looks cheap compared to other bonds with the same z-spread but no embedded options (for these options z-spread=oas). EASY WAY to understand, say we have two identical bonds, except one is callable and the other isn’t, and lets say option cost is 50bps. Both have a z-spread=150bps, however for the noncallable bond we know that Zspread=OAS=150bps. For the callable this implies the OAS=100bps or thought of another way this is the Zspread for this bond if it werent callable, i.e. now we can compare these bonds since we have spreads on the without the embedded options: Callable bond: OAS=100 Noncallable bond: OAS=150 This then implies that the noncallable bond is riskier because OAS only reflects credit and liquidity risk and so this bond would have to have a lower price than the callable bond. You can skip this explanation completely since its strictly intuitive and if you understood my mathematical “proof” above. Again my apologies for my earlier faux pas as I was thinking about things backwards and though the investor had a put option b/c I tend to wrongly think of the homeowner as the investor in these instances, and he is clearly not that he is the borrower/issuer! PS where did you see OAS>zpread for MBS? Just out of my own curiosity.

Right; the OASZ-spread for a put option because of the relation Z-spread-OAS=option cost, or if you prefer, Z-Spread=OAS+Option Cost. Stalla has a good answer for this: “Consider a non-callable bond whose price is P. The bond has a Z-spread of S. Now imagine that the bond suddenly becomes callable. The call feature implies that there may be future periods where the bond’s value is less than it would be if the bond had remained non-callable. Assuming that the bond’s price is unchanged at P, then its OAS must decline relative to the static spread so that the discounted present values of its future values (some of which may have ben reduced) is unchanged. So, for a callable bond, the OAS is generally less than the z-spread. However, suppose the embedded call option is deep out-of-the-money and the bond is unlikely to be called during its term. In this case, none of the bond’s future values are reduced by the “call rule” and so the OAS will equal the Z-spread. Because the embedded option can never be exercised to the bondholder’s benefit, the OAS will never be greater than the static spread.”

“Where you go wrong in your very first post is where you do the calculation for the MBS using the OAS and end up with 966.2, whereas when you used the zpread in the same calc you got 1000. because we know that for this problem zpread>oas this result is an impossibility, i.e the OAS calc should yield a value 1000 (if zpread yields 1000).” “Assuming that the bond’s price is unchanged at P, then its OAS must decline relative to the static spread so that the discounted present values of its future values (some of which may have ben reduced) is unchanged” Ahhh… So I was thinking about the OAS spread the wrong way. I was thinking that the call option would decrease the value of the bond (which it will) and this will increase the required discount rate (OAS). But I should have been assuming the price of the bond remains the same at $1000 (as we are comparing discount rates to this amount) and the discount rates adjust depending on the path of interest rates. To create the OAS. And under those rules the OAS will be less than the Z-Spread. Nice. I even created a little excel model to prove it. Thank-you for the help. Good luck in the exam. Re: adavydov7 - I didn’t see the OAS higher than the Z-spread anywhere- I just wanted to understand.